Analysis of Variance
Department of Educational Psychology
Agenda
1 Overview and Introduction
2 Introducing the Normal Curve
3 Calculating AUC for the Normal Distribution
4 The Standard Normal Distribution
5 Brief Example of Data ‘Coercion’
6 Conclusion
“All models are wrong, but some are useful” - George Box
Agenda
1 Overview and Introduction
2 Introducing the Normal Curve
3 Calculating AUC for the Normal Distribution
4 The Standard Normal Distribution
5 Brief Example of Data ‘Coercion’
6 Conclusion
\[ f(x) = \frac{1}{\sigma \cdot \sqrt{2 \cdot \pi}} \cdot e^{-0.50 \cdot (\frac{x - \mu}{\sigma})^2} \]
\[ f(x) = \frac{1}{b - a} \]
Agenda
1 Overview and Introduction
2 Introducing the Normal Curve
3 Calculating AUC for the Normal Distribution
4 The Standard Normal Distribution
5 Brief Example of Data ‘Coercion’
6 Conclusion
Agenda
1 Overview and Introduction
2 Introducing the Normal Curve
3 Calculating AUC for the Normal Distribution
4 The Standard Normal Distribution
5 Brief Example of Data ‘Coercion’
6 Conclusion
There is a special case of the normal distribution with more clearly specified characteristics: the standard normal distribution
The standard/standardized normal distribution is made up of z-scores, instead of whatever “raw” continuous values would be used
Agenda
1 Overview and Introduction
2 Introducing the Normal Curve
3 Calculating AUC for the Normal Distribution
4 The Standard Normal Distribution
5 Brief Example of Data ‘Coercion’
6 Conclusion
One misconception is that one can readily treat any continuous data as normal - this is not wise
Take for example class grade percentage data: {93, 92, 91, 90, 89, 94, 95, 96, 97}
Agenda
1 Overview and Introduction
2 Introducing the Normal Curve
3 Calculating AUC for the Normal Distribution
4 The Standard Normal Distribution
5 Brief Example of Data ‘Coercion’
6 Conclusion
The normal distribution is a useful and commonly used continuous variable distribution that meets several specific conditions. These characteristics make it readily predicable and applicable
Much like the other distributions and density functions, we can use the characteristics of the normal distribution to calculate AUC and understand the relative spread and placement of the data. This is aided by use of z-score and the standard normal curve as a special case
However, it is often mis-used and misunderstood, and we must take caution as we continue in the semester
Module 6 Lecture - Multiple Comparisons for Kruskal-Wallis || Analysis of Variance